Greece and Mexico took part in Youth Games. From Greece, the ratio of the number of female supporters to the number of male supporters was 1 : 4. From Mexico, the ratio of the number of female supporters to the number of male supporters was 1 : 2. The total number of supporters from Greece was ⁵₁₈ the total number of supporters from Mexico.

1. What was the ratio of the number of female supporters from Greece to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 40 female supporters from both countries joined the games, the percentage of all the male supporters became 64%. How many less male supporters from Greece than Mexico were there at first?

Greece		Mexico
5 u		18 u
Female supporters	Male supporters	Female supporters	Male supporters
1	4	1x2	2x2
1 u	4 u	6 u	12 u

(a)
Number of female supporters from Mexico
= ¹₃ x 18 u
= 6 u

Number of male supporters from Greece
= ²₃ x 18 u
= 12 u

Total number of female supporters
= 1 u + 6 u
= 7 u

Female supporters from Greece : Total female supporters
1 : 7

(b)

	Female supporters	Male supporters
Before	7x4 = 28%	16x4 = 64%
Change	+ 40
After	36%	64%

Number of female supporters in the end in percent
= 100% - 64%
= 36%

Total number of male supporters at first
= 4 u + 12 u
= 16 u

After another 40 female supporters from both countries joined the games, the percentage of all the male supporters became 64%.

Since only more female supporters joined the games, the number of male supporters remains unchanged. Make the number of male supporters the same.

16 u = 64%

1 u = 64% ÷ 16 = 4%

Number of female supporters at first in percent
= 7 x 4%
= 28%

Number of female supporters from both countries who joined the games
= 36% - 28%
= 8%

8% = 40 

1% = 40 ÷ 8 = 5

Number of less male supporters from Greece than Mexico at first
= 12 u - 4 u
= 8 u
= 8 x 4%
= 32%
= 32 x 5
= 160 

Answer(s): (a) 1 : 7; (b) 160